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<b>let </b><font color="Maroon">S</font> be  non <a href="struct_0.html#V3">empty</a> non <a href="msualg_1.html#V2">void</a>  <a href="msualg_1.html#L1">ManySortedSign</a> ;<br/><b>let </b><font color="Maroon">A1</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>, <font color="Maroon">A2</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>, <font color="Maroon">B1</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>, <font color="Maroon">B2</font> be    <a href="msualg_1.html#L3">MSAlgebra</a> of <font color="Maroon">S</font>;<br/>



<b>assume </b><a NAME="E1:6"/><i><font color="Green">E37</font></i>: 
(  <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A1</font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A1</font> #) <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">B1</font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">B1</font> #) &amp;  <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">A2</font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">A2</font> #) <a href="hidden.html#R1">=</a>  <a href="msualg_1.html#G3">MSAlgebra</a>(# the <a href="msualg_1.html#U4">Sorts</a> of <font color="Maroon">B2</font>,the <a href="msualg_1.html#U5">Charact</a> of <font color="Maroon">B2</font> #) )
 ;<br/>

<b>let </b><font color="Maroon">f</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">A1</font>,<font color="Maroon">A2</font>;<br/><b>let </b><font color="Maroon">g</font> be   <a href="msualg_3.html#NM1">ManySortedFunction</a> of <font color="Maroon">B1</font>,<font color="Maroon">B2</font>;<br/>



<b>assume </b><a NAME="E2:6"/><i><font color="Green">E41</font></i>: 
<font color="Maroon">f</font> <a href="pboole.html#R6">=</a> <font color="Maroon">g</font>
 ;<br/>

<b>let </b><font color="Maroon">o</font> be   <a href="msualg_1.html#NM2">OperSymbol</a> of <font color="Maroon">S</font>;<br/>

<b>assume </b><a NAME="E3:6"/><i><font color="Green">E52</font></i>: 
(  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">o</font>,<font color="Maroon">A1</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  &amp;  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">o</font>,<font color="Maroon">A2</font> <a href="hidden.html#NR2" target="_self">&lt;&gt;</a>  <a href="xboole_0.html#K1">{}</a>  )
 ;<br/>

<b>let </b><font color="Maroon">x</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">o</font>,<font color="Maroon">A1</font>;<br/><b>let </b><font color="Maroon">y</font> be    <a href="subset_1.html#M1">Element</a> of  <a href="msualg_1.html#K3">Args</a> <font color="Maroon">o</font>,<font color="Maroon">B1</font>;<br/>



<b>assume </b><a NAME="E4:6"/><i><font color="Green">E53</font></i>: 
<font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">y</font>
 ;<br/>

<a NAME="E5:6"/>
<font color="Maroon">f</font> <a href="msualg_3.html#K5">#</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <span class="p1">(<span class="default"><a href="pralg_2.html#K3">Frege</a> <span class="p2">(<span class="default"><font color="Maroon">f</font> <a href="funct_1.html#NK3" target="_self">*</a> <span class="p3">(<span class="default"><a href="msualg_1.html#K1">the_arity_of</a> <font color="Maroon">o</font></span>)</span></span>)</span></span>)</span> <a href="funct_1.html#K1">.</a> <font color="Maroon">x</font>
 
<b>by </b><i>, <a class="ref" href="msualg_3.html#D7">MSUALG_3:def 7</a></i>;<br/>
<b>hence </b><a NAME="E6:6"/>
<font color="Maroon">f</font> <a href="msualg_3.html#K5">#</a> <font color="Maroon">x</font> <a href="hidden.html#R1">=</a> <font color="Maroon">g</font> <a href="msualg_3.html#K5">#</a> <font color="Maroon">y</font>
 <b>by </b><i>, , , , <a class="ref" href="msualg_3.html#D7">MSUALG_3:def 7</a></i>;<br/>


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